Deterministically and Sudoku-Deterministically Recognizable Picture Languages

The recognizable 2-dimensional languages are a robust class with many characterizations, comparable to the regular languages in the 1-dimensional case. One characterization is by tiling systems. The corresponding word problem is NP-complete. Therefore, notions of determinism for tiling systems were suggested. For the notion which was called "deterministically recognizable" it was open since 1998 whether it implies recognizability. By showing that acyclicity of grid graphs is recognizable we answer this question positively. In contrast to that, we show that non-recognizable languages can be accepted by a generalization of this tiling system determinism which we call sudoku-determinism. Its word problem, however, is still in linear time. We show that Sudoku-determinism even contains the set of 2-dimensional languages which can be recognized by 4-way alternating automata

Searching paths of constant bandwidth

As a generalization of paths, the notion of paths of bandwidth w is introduced. We show that, for a given constant w >= 1, the corresponding search problem for such a path of length k in a given graph is NP-complete and fixed-parameter tractable in the parameter k, like this is known for the special case w=1, the LONGEST PATH problem. We state the FPT algorithm in terms of a guess and check protocol which uses witnesses of size polynomial in the parameter

Exponential Multiplication Schemes

We present an idea to describe a polynomial with 2^n distinct integer zeros by an n-tuple of integers via a scheme of n recurring equations. We call such an n-tuple an exponential multiplication scheme of size n. Exponential multiplication schemes of size 1,2,3, and 4 are presented. Under the assumption that fast exponential multiplication scheme generators exist we suggest a fast randomized heuristic for the factorization problem

Entre autoridad y libertad: el consenso, idea central de la teoría política de Nicolás de Cusa en el De concordantia catholica

In De concordantia catholica, Nicholas of Cusa develops two seemingly contradictory views of government. In book I, he derives all power from an upper source and builds up a monarchic conception of the Church and the State. Differently, in books II and III he stresses the dependence of government on the consent of subjects, which makes of him a pioneer of democratic formulations of government. The author of the article shows that Nicholas of Cusa (1) frames these two seemingly contradictory views within a broader theologic-christologic thesis. This thesis holds that all government must derive from both humane and divine sources, which allows the author to conclude that (2) Nicholas’s singular statements on the radical freedom of man (naturally a gift of God) and on the limitations –to be exerted by control commissions– of both ecclesiastical and temporal powers set the ground for the development of a democratic thought founded on human rights.En el De concordantia catholica, Nicolás de Cusa desarrolla dos lecturas aparentemente contradictorias del gobierno. En el libro I deriva todo el poder desde una fuente superior y construye una concepción monárquica de la Iglesia y el Estado. Y, de manera diferente, en los libros II y III subraya la dependencia del gobierno frente al consenso de sus súbditos, lo que lo convierte en un pionero de las formulaciones democráticas de gobierno. El autor de este artículo muestra que Nicolás de Cusa (1) enmarca estas dos lecturas aparentemente contradictorias dentro de una tesis más amplio de índole teológico-cristológico. Esta tesis sostiene que todo gobierno debe derivar tanto de fuentes divinas como humanas. Esta le permite concluir al autor que (2) Nicolás presenta singulares planteos respecto a la libertad radical del hombre (naturalmente, siendo esta un regalo de Dios) y respecto a las limitaciones –debe ser ejercida bajo comisiones de control– de los poderes tanto eclesiástico como temporal, que se instituyen como base teórica para el desarrollo de un pensamiento democrático basado en los derechos humanos